University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
Good strongly regular relations on weak $Gamma$-(semi)hypergroups
1
10
EN
M.
Jafarpour
Vali-e-Asr university of Rafsanjan
rmo4909@yahoo.com
H.
Aghabozorgi
Vali-e-Asr university of Rafsanjan
h_aghabozorgi1@yahoo.com
T.
Zare
Vali-e-Asr university of Rafsanjan
tahere_zare@yahoo.com
10.22124/jart.2017.2401
In this paper first we introduce the notion of weak $Gamma$-(semi)hypergroups, next some classes of equivalence relations which are called good regular and strongly good regular relations are defined. Then we investigate some properties of this kind of relations on weak $Gamma$-(semi)hypergroups.
(semi)hypergroup,weak $Gamma$-(semi)hypergroup,good regular relation
http://jart.guilan.ac.ir/article_2401.html
http://jart.guilan.ac.ir/article_2401_49e071441b8cb76d3181ccf5829d6819.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
Left I-quotients of band of right cancellative monoids
11
25
EN
N.
Ghroda
Al-Ghrabi University
nassraddin2010@gmail.com
10.22124/jart.2017.2402
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancellative monoids with certain conditions.
I-orders,I-quotients,right cancellative monoid,inverse hull
http://jart.guilan.ac.ir/article_2402.html
http://jart.guilan.ac.ir/article_2402_6a9e9726321356602bbe3cb751ec727a.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
Exact annihilating-ideal graph of commutative rings
27
33
EN
P. T.
Lalchandani
Sauarshtra University
finiteuniverse@live.com
10.22124/jart.2017.2400
The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
Annihilating-ideal graph,exact annihilating-ideal,exact annihilating-ideal graph
http://jart.guilan.ac.ir/article_2400.html
http://jart.guilan.ac.ir/article_2400_aaf79abadd18993bb61e46b076b4b125.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
A new branch of the logical algebra: UP-algebras
35
54
EN
A.
Iampan
0000-0002-0475-3320
University of Phayao
aiyared.ia@up.ac.th
10.22124/jart.2017.2403
In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a generalization of KU-algebras.
UP-algebra,UP-ideal,congruence,UP-homomorphism
http://jart.guilan.ac.ir/article_2403.html
http://jart.guilan.ac.ir/article_2403_1c3ccde59fb8f4d45495220124df4b3a.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
Properties of extended ideal based zero divisor graph of a commutative ring
52
59
EN
K.
Porselvi
Karunya University
porselvi94@yahoo.co.in
R.
Solomon Jones
Karunya University
jonesrooneya@gmail.com
10.22124/jart.2017.2404
This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.
Commutative rings,ideals,prime ideals,zero-divisor graph
http://jart.guilan.ac.ir/article_2404.html
http://jart.guilan.ac.ir/article_2404_5fcd793296350fc946528bcb35707617.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
5
1
2017
06
01
A Note on a graph associated to a commutative ring
61
82
EN
S.
Visweswaran
Saurashtra University
s_visweswaran2006@yahoo.co.in
J.
Parejiya
Saurashtra University
parejiayjay@gmail.com
10.22124/jart.2017.2399
The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $chi(G(R)) = omega(G(R))< infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.
Comaximal graph of a ring,complete graph,chromatic number,clique number,planar graph
http://jart.guilan.ac.ir/article_2399.html
http://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf